A Family Of Local Repair Codes Based On Strongly Symmetric Self Orthogonal Sudoku

Locally repairable codes(LRC)is a class of erasure codes.LRC are welcomed in distributed storage systems(DSS)for encoding and storage.There are two ways to repair multi failed nodes:1)parallel mode,in which all the failed nodes can be repaired by other nodes at once;2)sequential mode,in which failed nodes are repaired one by one,and previously repaired node can be uesd to repair other failed noeds.In this thesis,we aim at(n,k,r,t,u)—Exact locally repairable codes,which are[n,k]linear codes with the property that any set of failed nodes of size at most t can be simultaneously repaired in parallel mode,and all failed nodes of size at most u can be sequentially repaired by r(r<k)other coordinates.We construct a family of local repair codes based on strongly symmetric self orthogonal sudoku.Our construction is based on the work of Ehsan Yavari and Morteza Esmaeili.The construction of sudoku is based on the work of Xuyan Shao etc.We improve the information rate of the code and give an algorithm to construct them.